There are two locations for fuse boxes on a 2005 Cobalt. 1) is under the hood,on the driver's side,under the jump start contact. 2) is inside the center console,on the right side. The forward part of the console kick panel has a press-opening panel,which,when removed,reveals the fuse box. Posted on Jul 14,2014. Fuse box location 2005 chevy cobalt - Fixya Was this helpful?